The girls' bicycles and a purse were found near Meyers Lake hours after they were reported missing. Scent dogs following the girls' trail led searchers around the lake and stopped at the water's edge, Cook-Morrissey said.

Authorities are draining the lake, but the operation is taking longer than originally expected.

"They don't swim there. My daughter is familiar with swimming in lakes, so I don't think she would be scared of this lake, but they don't come here and swim here," she said.

Cook-Morrissey said she'd be "more comfortable" with the theory that the girls might have been abducted "once they drain the lake and we find nothing there."

"If you've taken our kids," she said on national TV, "bring them back."

The FBI brought two dogs to the area to search Monday night, spokeswoman Sandy Breault said. Authorities did all they could with the dogs, and the animals won't be used again unless there is a new development, she said.

Authorities said Tuesday that they didn't know whether the girls had been at the lake.

"We have their bicycles, and we have the purse, and that doesn't tell me that they've been there, just that those items are there," Abben said.

The family has been questioned and polygraphed and had information taken from their cell phones, a process Cook-Morrissey said is hard but necessary.

"We know that it's a necessary measure they have to take to get as much information as they can and of course rule us out, so we did what we have to do," she said.

Questioning has taken Cook-Morrissey and other family members away from the lake, which is hard, she said.

"Not that being out here might make a difference, but in your heart you want to be close to where they were last seen," she said.

When Deutsch heard that two little girls were missing in his town, he said, the first thing he did was to make sure every city asset that was needed was made available to the county sheriff.

The next thing he did was take to the air, taking off in his twin-engine plane and flew over his town, looking for any sign of Lyric and Elizabeth.

"It just makes you sick," said Deutsch, who knows both families.

In this town, neighbors know exactly how many people live there -- 4,751 -- and the small community has never suffered through anything like the worrying going on now, the mayor said.

The search remains a missing persons case, authorities said. No evidence has been found to suggest this is a crime, Deutsch said, but it is a mystery that has the whole community looking for two of their own.

"We just want our girls home," Tammy Brousseau, an aunt to both girls, told CNN's "AC360˚." "We're bracing for the worst but hoping for the best."

Calls are coming in to a tip line, Abben said, and each bit of information is being checked out. Police ask that anyone who may have seen the girls on Friday contact authorities.

Lyric's grandmother Wylma Cook said she doesn't believe that the girls intended to go swimming.

"I don't think they would have even known the way to Meyers Lake," she told HLN's Nancy Grace on Tuesday.

Heather Collins, Elizabeth's mother, told HLN's Jane Velez-Mitchell that if the girls were abducted, she would not pass judgment. "We just want our children brought back," she said.